g(x)
graph of sine function which starts at 0 comma 0 and decreases to thegraph of sine function which starts at 0 comma 0 and decreases to the minimum pi over 2, then increases to the maximum of 3 pi over 2 then decreases to 2 pi where the cycle repeats. Courtesy of Texas Instruments (graph attached)
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.
We look for the minimum of each function. For f (x) = 3x2 + 12x + 16: We derive the function: f '(x) = 6x + 12 We match zero: 6x + 12 = 0 We clear the value of x: x = -12/6 x = -2 We substitute the value of x in the equation: f (-2) = 3 * (- 2) ^ 2 + 12 * (- 2) + 16 f (-2) = 4 For g (x) = 2sin(x-pi): From the graph we observe that the minimum value of the function is: y = -2 Answer: A function that has the smallest minimum y-value is: y = -2
